On the Cauchy transform of complex powers of the identity function

Benjamin Faktor, Michael Kuhn, Gahl Shemy

The integral ${\int }_{|z|=1}\frac{z^{\beta }}{z-\alpha }dz$ for $\beta =\frac{1}{2}$ has been comprehensively studied by Mortini and Rupp for pedagogical purposes. We write for a similar purpose, el…